This page describes several situations in which dialing this toll free number may not work:
-calling from a cell phone
-payphones
-hotel phones

It also says that toll free dialing may be blocked from some phones. With all these possible reasons I can't tell you why the call won't go through.

My suggestion is to try the Santiago number provided: (2)712-6464. If your parents are in Santiago they most likely have to leave out the starting 2 which is the area code. If outside Santiago try dialing the number as it is and, if it doesn't work try adding a zero before 2: 02 712 6464.

Thanks Dan. I passed this information along to them via email.. I hope they have some luck. I have a feeling the problem was they didn't prefix the Santiago number with a 0, which I only learned about after visiting this page: https://www.howtocallabroad.com/codes.html

As far as the toll-free number that is listed on the calling card, do you have any ideas how it should be dialed? Maybe drop the 116 and just dial starting from 800? or prefix the 116 with a 0? or drop the 116 and prefix the 800 with a 0? The 116 in that number just seems odd to me.

Toll free numbers in Chile are preceded by the area code. For example a 800 number in Santiago has the following format: 2 800 ??? ???. There is no area code 116 - this is probably a national dialing code of some sort. If they list it there it's likely for a reason. Try adding a zero before 116 to see what happens. Don't forget however that there is a possibility that the phone your parents use doesn't work with toll free numbers. Let me know what happens.